A token is a physical element which has unique properties which enable the token to be used for identification and authentication purposes, and for the generation of encryption/decryption keys. Such tokens are known in the art and typically comprise a physical object that comprises the unique physical element which enables a probing device to probe the unique physical element and to obtain a unique response from this unique physical element caused by the probing. The unique physical element is also often referred to as the physical unclonable function or physical random function or physical one-way function. This unique response from the physical unclonable function may be used by the probing device to generate a specific bit string which may indicate that the token is authentic. Alternatively, the bit string may be used, for example, to encrypt or decrypt data. Many different examples of physical unclonable functions are known in the art, such as three-dimensional optical media comprising scattering elements which are distributed randomly and which generate a unique scattering distribution when illuminated with, for example, a laser beam.
Physical unclonable functions may also be constituted by a capacitor comprising a dielectric medium arranged between the electrodes of the capacitor, in which the dielectric medium comprises a distribution of conducting particles. Such physical unclonable functions are, for example, known from WO 2007/069190 titled, “On-Chip Estimation of Key-Extraction Parameters for Physical Tokens,” of Geert Schrijen et al. (published Jun. 21, 2007). Because both the distribution of the conducting particles in the dielectric medium and the shape of the individual conducting particles are substantially random, the capacitance measured from the capacitor being the physical unclonable function is also substantially random. A benefit when using the physical unclonable function constituted by a capacitor is that it enables the physical unclonable function to be relatively easily embedded in a chip, for example, on a smart card and used, for example, in secure transactions.
A problem with such known physical unclonable functions constituted by a capacitor is that a bandwidth within which the randomness of the capacitance varies is relatively limited.